Respuesta :
Answer:
y = 2x-3
Explanation:
By definition, two lines are parallel if they have the same slope.
Given the equation for a line:
[tex]y=2x-1[/tex]Comparing the given line with the slope-intercept form of a line:
[tex]\begin{gathered} y=mx+b \\ \implies\text{Slope of the line, m=2} \end{gathered}[/tex]Thus, we want to find the equation of the line with the following properties:
• Slope: m = 2
,• Point: (x1,y1)=(2,1)
In order to do this, we employ the use of the point-slope form of the equation of the line:
[tex]\begin{gathered} y-y_1=m\mleft(x-x_1\mright) \\ \implies y-1=2(x-2) \end{gathered}[/tex]We then simplify:
[tex]\begin{gathered} y-1=2x-4 \\ Add\text{ 1 to both sides of the equation} \\ y-1+1=2x-4+1 \\ y+0=2x-3 \\ y=2x-3 \end{gathered}[/tex]The equation of the parallel line is y=2x-3.
